Russia 11 класс Physics (advanced)

1. Magnetic field

Magnetic induction · Ampère and Lorentz forces · Magnetic materials

• Magnetic Field due to a Current: Biot-Savart Law and Ampere's Law – A current makes a magnetic field around it (Oersted, 1820). The Biot-Savart law gives the field of a tiny piece of wire: dB = (μ₀/4π)·I dl sinθ / r². Adding all pieces of a circular loop gives B = μ₀NI / 2R at the centre and μ₀NIR² / 2(R² + x²)^{3/2} on the axis. Ampere's circuital law ∮B·dl = μ₀I gives B = μ₀I / 2πr for a long straight wire. A long solenoid has a strong, uniform field B = μ₀nI inside and almost none outside.
• Lorentz Force, Torque on a Loop and the Moving Coil Galvanometer – A charge q moving with velocity v feels F = q(E + v × B), the Lorentz force. The magnetic part qvB sinθ is at right angles to v, so it bends the path into a circle (r = mv/qB) without changing speed. A wire feels F = IL × B. Parallel wires attract if the currents are in the same direction: F/L = μ₀I₁I₂/2πd. A loop in a field feels a torque τ = m × B with magnetic moment m = NIA, so a loop acts as a magnetic dipole. A moving coil galvanometer uses this torque: its deflection φ = (NAB/k)I. A small shunt turns it into an ammeter; a large series resistance turns it into a voltmeter.
• Magnetism and Matter – A bar magnet behaves like a solenoid: tiny current loops of electrons inside it line up. Its field on the axis (2m/r³ form) is twice the field on the equator at the same distance, and points the other way. In a uniform field a magnet feels a torque τ = m × B that turns it to line up with B. Field lines are closed loops that never cross. Materials react differently: diamagnetic ones are pushed out of a field (χ small and negative), paramagnetic ones are pulled in weakly (χ small and positive), ferromagnetic ones are pulled in strongly (χ very large). Magnetisation M is the magnetic moment per unit volume; B = μ₀(H + M), χ = M/H, μᵣ = 1 + χ. Heating reduces magnetism: paramagnets follow Curie law χ = C/T, and a ferromagnet turns paramagnetic above its Curie temperature.

2. Electromagnetic induction

Faraday's law · Self-induction

• Electromagnetic Induction – When the magnetic flux through a coil changes, an emf is produced in it: ε = −N dΦ/dt (Faraday). The minus sign is Lenz's law: the induced current always opposes the change that made it. Moving a rod in a field gives motional emf ε = Blv. A changing current makes an emf in its own coil (self-induction, L) and in a nearby coil (mutual induction, M).
• Force on a Current-Carrying Conductor, Motor and Induction – A wire carrying current inside a magnetic field feels a push. The push is biggest when the wire is at 90° to the field and zero when it is parallel. Fleming's left-hand rule gives its direction. A motor uses this push to spin a coil; a generator does the reverse and makes current by moving a coil or magnet.

3. Mechanical oscillations

Harmonic oscillations

• Simple Harmonic Motion (SHM) – A motion that repeats after a fixed time is periodic. If the object goes to and fro about a middle point and the force pulling it back is proportional to its distance from the middle (F = −kx), the motion is simple harmonic. Its position is x = A sin(ωt + φ), with ω = 2π/T = 2πf. Speed is largest in the middle, acceleration is largest at the ends, and total energy ½kA² stays constant.

4. Electromagnetic oscillations

LC circuit · AC circuits

• LC Oscillations – An LC circuit is a capacitor (C) joined to a coil (L). A charged capacitor pushes current through the coil; the coil keeps the current going and charges the capacitor the other way. Energy swings between the electric field of the capacitor and the magnetic field of the coil. With no resistance the swing never stops. Its period is T = 2π√(LC) (Thomson formula) and its frequency is f = 1 / (2π√(LC)). Resistance makes the oscillations damped; a generator with a transistor tops up energy to keep them going.
• Alternating Current – An alternating current (AC) changes size and direction again and again: I = I₀ sin ωt. Its rms value is I₀/√2, the steady DC that gives the same heating. A resistor keeps V and I in step; an inductor makes I lag by 90° (Xʟ = ωL); a capacitor makes I lead by 90° (Xᴄ = 1/ωC). In a series LCR circuit Z = √(R² + (Xʟ − Xᴄ)²), resonance happens when Xʟ = Xᴄ, and average power is P = Vrms Irms cos φ.
• Force on a Current-Carrying Conductor, Motor and Induction – A wire carrying current inside a magnetic field feels a push. The push is biggest when the wire is at 90° to the field and zero when it is parallel. Fleming's left-hand rule gives its direction. A motor uses this push to spin a coil; a generator does the reverse and makes current by moving a coil or magnet.

5. Waves

Mechanical waves and sound · Electromagnetic waves

• Progressive Waves: Types, Speed and Equation – A wave carries energy from place to place without carrying the matter along. In a transverse wave the particles move at right angles to the wave; in a longitudinal wave they move along it. Speed v = fλ. On a string v = √(T/μ); for sound in a gas v = √(γP/ρ). A wave moving along +x is y = A sin(kx − ωt), with k = 2π/λ and ω = 2πf.
• Electromagnetic Waves – A changing electric field acts like a current, called the displacement current, and it makes a magnetic field. A changing magnetic field makes an electric field. Together they travel as an electromagnetic (EM) wave at c = 3 × 10⁸ m/s, even through empty space. E and B are at right angles to each other and to the direction of travel, so EM waves are transverse. Sorted by wavelength, they form the spectrum: radio, microwave, infrared, visible, ultraviolet, X-rays and gamma rays.

6. Optics

Geometric optics · Lenses and optical instruments · Wave optics

• Spherical Mirrors and the Mirror Formula – A spherical mirror is a piece cut from a shiny ball. Its focal length is half its radius of curvature (f = R/2). With the Cartesian sign convention, the object distance u, image distance v and focal length f are linked by 1/v + 1/u = 1/f, and the magnification is m = h′/h = −v/u. Concave mirrors have negative f; convex mirrors have positive f.
• Thin Lenses: Lens Maker's Formula, Lens Formula and Power – At one curved surface, n₂/v − n₁/u = (n₂ − n₁)/R. Two such surfaces make a thin lens with 1/f = (n − 1)(1/R₁ − 1/R₂) (lens maker's formula). Object and image distances follow 1/v − 1/u = 1/f, magnification m = v/u, power P = 1/f (in dioptres when f is in metres), and thin lenses in contact add their powers: P = P₁ + P₂.
• Interference (Young's Double Slit) and Single Slit Diffraction – Two coherent sources (same frequency, fixed phase difference) make a steady pattern of bright and dark fringes. At a point on the screen the path difference is Δ = yd/D: bright where Δ = nλ, dark where Δ = (n + ½)λ. All fringes have equal width β = λD/d. A single slit of width a gives diffraction: a bright central maximum of width 2λD/a, with first minima where a sin θ = λ, and weaker side maxima.

7. Special relativity

Relativity

• Special Relativity – Special relativity (Einstein, 1905) rests on two postulates: the laws of physics are the same in all inertial frames, and the speed of light in a vacuum, c ≈ 3.00 × 10⁸ m/s, is the same for every observer. It follows that moving clocks run slow (t = γt₀), moving objects are shorter along their motion (L = L₀/γ), and mass is a form of energy (E = mc²), with γ = 1/√(1 − v²/c²). At everyday speeds γ ≈ 1, so Newton's mechanics works; near c it fails.

8. Quantum physics

Wave–particle duality · Atomic physics · Nuclear and particle physics

• Photoelectric Effect and Einstein's Equation – When light of high enough frequency falls on a metal, electrons jump out at once. Light comes in packets called photons, each with energy E = hν. One photon gives all its energy to one electron: hν = φ + KEmax, where φ is the work function. Below the threshold frequency ν₀ = φ/h no electron comes out, however bright the light.
• Atoms: From Alpha Scattering to the Bohr Model – Rutherford shot alpha particles at thin gold foil and found that an atom is mostly empty, with a tiny, heavy, positive nucleus in the middle. Bohr then said the electron in hydrogen can move only on fixed orbits where its angular momentum is nh/2π. In orbit n the radius is 0.529 n² Å, the speed is (2.19 × 10⁶)/n m/s and the energy is −13.6/n² eV. When the electron jumps down, the energy difference comes out as light of one exact colour, which gives the line spectrum of hydrogen.
• Nuclei: Size, Nuclear Force, Binding Energy, Fission and Fusion – A nucleus is made of Z protons and N neutrons (A = Z + N nucleons). Its radius is R = R₀A^(1/3) with R₀ ≈ 1.2 fm, so every nucleus has almost the same huge density. A very strong, short-range nuclear force holds the nucleons together. The nucleus weighs a little less than its loose parts; this mass defect Δm is the binding energy, E = Δm c² (1 u = 931.5 MeV). Binding energy per nucleon is highest near iron (A ≈ 56), so heavy nuclei give energy when they split (fission) and light nuclei give energy when they join (fusion).

9. Astronomy and astrophysics

Methods of astronomy · Solar System and stars · Galaxies and cosmology

• Stars: Colour, Brightness, Distance and the H-R Diagram – A star is a huge ball of hot gas that shines by nuclear fusion. Its colour shows its surface temperature: red stars are cool, blue stars are hot (Wien's law: λmax × T = 2.9 × 10⁻³ m K). Stars are sorted into spectral classes O B A F G K M, hottest to coolest. How bright a star looks (apparent magnitude) depends on its real power (luminosity) and its distance, because light weakens as 1/d². Nearby distances are found by parallax: d (pc) = 1/p (arcsec). Luminosity depends on size and temperature (L = 4πR²σT⁴). The H-R diagram plots luminosity against temperature and shows the main sequence, giants and white dwarfs.
• Cosmology: The Expanding Universe and the Big Bang – Cosmology is the study of the whole universe: its structure, history and future. Galaxies gather in groups, clusters and filaments around huge voids. Distant galaxies are moving away from us, faster the farther they are (Hubble's law, v = H₀d), because space itself is expanding. Running the expansion backwards leads to a hot, dense beginning about 13.8 billion years ago, the Big Bang. The main evidence is redshift, the cosmic microwave background and the amounts of hydrogen and helium. Most of the universe is dark matter and dark energy.

10. Physics practicum and review

Practicum and review

Coming soon